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3 years ago

A bookcase has 6 shelves.

Mathematics

2 answers:

Bezzdna [24]3 years ago

6 0

Answer:

21 books

Step-by-step explanation:

130-4=x

x/6= answer

timurjin [86]3 years ago

4 0

The answer would be 21 books

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Plz help with full process

BabaBlast [244]

Answer:

$\displaystyle \frac{(a - b)^{2} - {c}^{2} }{{a}^{2} - {(b+ c)}^{2} } + \frac{(b - c)^{2} - {a}^{2} }{{b}^{2} - {(c+ a)}^{2} } + \frac{(c - a)^{2} - {b}^{2} }{{c}^{2} - {(a+ b)}^{2} }=1$

Step-by-step explanation:

Algebra Simplifying

We are given the expression:

$\displaystyle T=\frac{(a - b)^{2} - {c}^{2} }{{a}^{2} - {(b+ c)}^{2} } + \frac{(b - c)^{2} - {a}^{2} }{{b}^{2} - {(c+ a)}^{2} } + \frac{(c - a)^{2} - {b}^{2} }{{c}^{2} - {(a+ b)}^{2} }$

We need to repeatedly use the following identity:

$(a^2-b^2)=(a-b)(a+b)$

For example, the first numerator has a difference of squares thus we factor as:

$(a - b)^{2} - {c}^{2} =(a-b-c)(a-b+c)$

The first denominator can be factored also:

${a}^{2} - {(b+ c)}^{2} = (a-b-c)(a+b+c)$

Applying the same procedure to all the expressions:

$\displaystyle T=\frac{(a - b- c)(a-b+c) }{a-b-c)(a+b+c) } + \frac{(b - c - a)(b-c+a) }{(b-c-a)(b+c+a) } + \frac{(c - a-b)(c-a+b) }{(c-a-b)(c+a+b)}$

Simplifying all the fractions:

$\displaystyle T=\frac{a - b- c}{a+b+c} + \frac{b-c+a}{b+c+a } + \frac{c-a+b }{c+a+b}$

Since all the denominators are equal:

$\displaystyle T=\frac{a - b+ c+b-c+a+c-a+b}{a+b+c}$

Simplifying:

$\displaystyle T=\frac{a +c+b}{a+b+c}$

Simplifying again:

T = 1

Thus:

$\boxed{\displaystyle \frac{(a - b)^{2} - {c}^{2} }{{a}^{2} - {(b+ c)}^{2} } + \frac{(b - c)^{2} - {a}^{2} }{{b}^{2} - {(c+ a)}^{2} } + \frac{(c - a)^{2} - {b}^{2} }{{c}^{2} - {(a+ b)}^{2} }=1}$

8 0

3 years ago

Read 2 more answers

Katie had four more dimes than quarters in her pocket, for total of $2.10. Which equation could be used to determine the number

Lera25 [3.4K]

If quarters represents x, then let 4x represent dimes. (there are 4 more times dimes than quarters)

x + 4x = $2.10

5x = $2.10

x = .42

Check your answer.

5 (.42) = $2.10 Yes! It checks out.

6 0

3 years ago

ΔRST is dilated about the origin, O, to create ΔR'S'T'. Point R is located at (3, 9), and point R' is located at (1.2, 3.6). Whi

motikmotik

Answer 
scale factor=0.4

Explanation 
The scale factor for any transformation is the ration of the image distance to the object distance.
That is the ratio of distance from the origin to the image to the distance from the origin to the object.
In the case above, OR’is the image distance and OR is the object distance.
OR’ = √(〖1.2〗^2+〖3.6〗^2 )=√14.4=3.794733192
OR = √(3^2+9^2 )=√90=9.486832981

The scale factor = 3.794733192/9.486832981
=0.4

5 0

3 years ago

Read 2 more answers

Complete the table.

ElenaW [278]

Answer:

a = 1/2

b = 1

c = 3/2

d = 1

e= 0

f = -1

Step-by-step explanation: right on edg

6 0

4 years ago

V/2+6=14 here u go for my math people

suter [353]

Simple enough:
Solve for V:
V/2 + 6 = 14

Put each term in V/2 + 6 over the common denominator 2: V/2 + 6 = V/2 + 12/2:
V/2 + 12/2 = 14

V/2 + 12/2 = (V + 12)/2:
(V + 12)/2 = 14

Multiply both sides of (V + 12)/2 = 14 by 2:
(2 (V + 12))/2 = 2×14

(2 (V + 12))/2 = 2/2×(V + 12) = V + 12:
V + 12 = 2×14

2×14 = 28:
V + 12 = 28

Subtract 12 from both sides:
V + (12 - 12) = 28 - 12

12 - 12 = 0:
V = 28 - 12

28 - 12 = 16:

Answer: V = 16

3 0

3 years ago

Read 2 more answers